Calibration of A Five-Hole Probe in Null and Non-Null Technique

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1 ISSN: , Vol. 6, Issue, (Part - 7) May 16, pp.27-2 RESEARCH ARTICLE OPEN ACCESS Calibration of A Five-Hole Probe in Null and Non-Null Technique Ratneswar Majumdar a,. Chowdhury b, P.K. Sinha c and B. Majumdar b a epartment of Civil Engineering, Calcutta Institute of Engineering & Management, Kolkata. India b epartment of Power Engineering, Jadavpur niversity, Kolkata. India c epartment of Mechanical Engineering, urgapur Institute of Advanced Technology & Management, urgapur, India. ABSTRACT The analysis of fluid flow is encountered in almost all engineering applications. Flow measurements, particularly velocity and its direction, turbulence quantities are needed in order to improve the understanding of various complex flow phenomena and to validate and further refine the computer flow models. Pressure probes find wide application in the measurement of fluid flows both in the laboratory and in the industry. A five-hole pressure probe is calibrated in both null and non-null technique. An algorithm for five-hole probe in non-null method is developed which utilizes a database of calibration data and a local least-squares interpolation technique is used for interpolation of flow properties. It is also found out that the non-null method was superior in ease of use and prediction of flow measurement variables than the null method. Keywords: five-hole probe, non-null method, interpolation technique, regression model, sector scheme. Nomenclature C Pitch angle coefficient C Yaw angle coefficient f1, f2, f, F(α), k Calibration constants G Acceleration due to gravity(m/s 2 ) Mean velocity (m/sec) X Velocity in x-direction (m/sec) Y Velocity in y-direction (m/sec) Z Velocity in z-direction (m/sec) C Ptotal Total pressure coefficient C Pstatic Static pressure coefficient P Pressure sensed by different holes Pitch angle () Yaw angle () ensity ( kg/m ) m ensity of manometric fluid (kg/m ) air ensity of air (kg/m ) Subscripts 1, 2,,,, 6, 7 Hole numbers I i th data point in a given sector egree Superscripts Average I. INTROCTION Multi-hole pressure probes have, over the years, been used to resolve the three-dimensional velocity vector and static and total pressures at the point of measurement in a flow field. Such devices include three-hole, five-hole and seven-hole probes and other combination of more tubes/holes. There are of course other types of pressure probes such as pitot-static probes and yaw probes, which, however, are not of interest here, since they cannot resolve all three components of the velocity vector. The application of five-hole probe was developed in 191 by Admiral Taylor. However, Pien [1] was first to show theoretically that for a spherical probe the velocity component in any plane in space can be obtained independently from three pressure measurements in that plane. Kjelgaard [2] developed a theoretical relationship and generalized it for a hemispherical tipped fivehole probe. Treaster and Yocum [] reported the non- nulling calibration technique and the interpolation procedure for commercially available prism and angle tubes probes made of five 1.27mm diameter hypodermic tubes. Mukhopadhya et. al. [] conducted experiments on hemispherical, conical and open ended five-hole probes to determine the effect of calibration coefficients on each of the probe tip shapes. Pisasale and Ahmed [] assumed potential flow theory across a spherical probe tip and presented a theoretical basis for extending the range of flow angles of a five-hole probe. The method assists in overcoming the singularity in calibration of five-hole probes for different 27 P a g e

2 ISSN: , Vol. 6, Issue, (Part - 7) May 16, pp.27-2 geometrical shapes, but the prediction errors remains of same magnitude as of the conventional method. A simplified method for measurement of - flow using -hole pressure probe has been discussed by Sitaram and Treaster [6]. II. EXPERIMENTAL SET P AN ALGORITHM FOR NON- NLL METHO WITH SECTOR SCHEME Schematic diagram of the experimental set up used for this study is shown in Fig.1. The main components of the experimental set up include an air supply unit, flow control arrangement, settling chamber, contraction cone and a straight test section. Every component, except the air supply unit and the straight test section were made of wood. The straight test section was made of transparent plexiglass. However, calibration is done in the open jet of air coming out from the test section. Ambient air is used as flowing fluid during calibration. A hemispherical tip five-hole pressure probe as shown in Fig.2 has been used for the calibration. It consists of five stainless steel tubes of outer diameter 1.2mm and inner diameter of.9mm glued together. The length of the five-hole pressure probe is.2m. A probe traversing gear has been designed for the present study, which allows the rotation of the probe in both pitch and yaw plane [8]. A simple regression method of matrix terms as discussed by Netter and Washerman [7] has been used in the present study for determining the different calibration coefficients as required. Fig.2. Schematic diagram of the pressure probe The sector method divides the entire calibration zone into five parts, one central zone and four side zones.the zones are chosen based on the highest pressure sensed by the holes e.g. when center hole senses maximum pressure, zone 1 is taken. etailed view of the probe with zonal discrimination is given in Fig. (a-b). (a) Section view with hole nomenclature Fig.1. Schematic diagram of experimental setup (b) ifferent sectors chosen Fig.. Sectoring scheme chosen for five-hole probe (hole numbers 1to ) 28 P a g e

3 ISSN: , Vol. 6, Issue, (Part - 7) May 16, pp.27-2 The calibration coefficients in various zones are defined as follows. ZONE1 P P ) P 2 P1 P C ) C ( P2 P ) C static ) pstatic total 1) ZONE P ) P 1 P P C 2 ) ) C 1 C static ) pstatic total ) ZONE P ) P 1 2 P P ( P2 P ) C ) C 1 ZONE2 ( P1 P P ) P P2 P C 2 ) ( P P ) C C static ) pstatic total 2) ZONE P ) P 1 P P C 1 ) ) C C static ) pstatic total ) C static ) pstatic total ) For all the above equations the value of should not be negative or too small. The first step is to determine the pressure hole that gives the maximum reading and accordingly to determine the zone where the probe lies. While calibrating the value of P s and P T are recorded and C α C β, Cp static and Cp total are thereby calculated for each zone. A full fourth order multiple regression model [8] with two independent variables, C α C β, that would predict four different variables (,, Cp static and Cp total ) depending on the coefficient set selected. The described regression model also applies for compressible flow and the nature of equation can be varied as order of the curve fit or the accuracy level by comparing the predicted data with the measured data. The multiple regression model does predict α and β explicitly but predicts the total pressure and static pressure implicitly via a pressure coefficient Cp static and Cp total, which are defined in each zone separately. This method of zonal division reduces large errors due to extrapolation. The zonal demarcation angles are chosen such that zones overlap e.g. hole 1 is maximum within yaw angles of ± 18 at a pitch angle of -9. The actual data prediction equations for the multiple regression model is defined as follows. α = Kα + Kα 1 C α +Kα 2 C β +Kα C α 2 +Kα C α C β +Kα C β 2 +Kα 6 C α +Kα 7 C α 2 C β +Kα 8 C α C β 2 +Kα 9 C β +Kα C α +Kα 11 C α C β +Kα 12 C α 2 C β 2 +Kα 1 C α C β +Kα 1 C β (1) β = K β + K β1 C α +K β2 C β +K β C 2 α +K β C α C β +K β C 2 β +K β6 C α +K β7 C 2 α C β +K β8 C α C 2 β +K β9 C β +K β C α +K β 11 C α C β +K β C α C β +K β1 C α C β +K β1 C β. (2) 2 Cp S = K CPS + K CPS1 C α +K CPS2 C β +K CPS C α +K CPS C α C β +K CPS C 2 β +K CPS6 C α +K CPS7 C 2 α C β +K CPS8 C α C 2 β +K CPS9 C β +K CPS 2 2 C α +K CPS11 C α C β +K CPS12 C α C β +K CPS1 C α C β +K CPS1 C β () 29 P a g e 2 Cp T = K CPT + K CPT1 C α +K CPT2 C β +K CPT C α +K CPT C α C β +K CPT C 2 β +K CPT6 C α +K CPT7 C 2 α C β +K CPT8 C α C 2 β +K CPT9 C β +K CPT 2 2 C α +K CPT11 C α C β +K CPT12 C α C β +K CPT1 C α C β +K CPT1 C β ().... The calibration coefficients are determined using matrix operations which automatically involves a least-square curve fit. The following matrices were defined

4 ISSN: , Vol. 6, Issue, (Part - 7) May 16, pp.27-2 Where, A is one of the flow properties like α, β, Cp static or Cp total. A sample set of N data points are taken for each of the given zone (a minimum of 1 sample points are required for uniquely defining the 1 K s). The K s are the calibration constants where the subscript identifies the term in expansion. The above equation could be abbreviated as follows [A]=[C][K]. () Where, [N 1], [A] matrix contains N values of one of the four flow properties, the [N 1], [C] matrix contains the corresponding expanded pressure coefficient variables, and the [ 1], [K] matrix contains the calibration coefficients. uring calibration the quantities within the A matrix are determined for every zone i.e. for α= and β=, the value of C α and C β at that point corresponding to Cp static and Cp total. The calibration constants are unique for every probe and are determined by solving the above matrix equation as outlined by Netter and Wasserman [8]. technique. The calibration constant and methods adopted are according to Byre and Pankhurst [9]. Fig.a shows the variation of pitch angle (α) versus the ratio of pressure (P -P 2 / P -P ). A first order polynomial function is generated to interpolate the pitch angle on the basis of the pressure sensed by holes 2,, and when the probe is inserted to an unknown flow. Fig.b shows the variation of pitch with the constant k. A second order polynomial function is generated to define k with respect to pitch angle. When the probe is inserted to an unknown flow the value of pitch angle interpolated earlier will thus provide the value of k. Fig.c shows the variation of F(α) with pitch angle. F(α) represents the dimensionless pressure coefficient. A second order polynomial function is generated to define the F(α) with respect to pitch angle. When the probe is inserted to an unknown flow the value of pitch angle interpolated earlier will thus provide the value of F(α). [K]= [C T C] -1 [C] T [A] (6) Equations (1) to () is then solved which gives the interpolated values of α, β, Cp static and Cp total values. All data points obtained during calibration were cross checked to ensure the effectiveness of the calibration constants obtained by using the pressures and calibration constant as inputs and flow angle as outputs. The interpolated values are then compared with the measured points and any questionable data points found are neglected. The calibration constants are again determined until a ±.6 accuracy level was reached for both pitch and yaw angles. Resolving the velocity vector in the mutually perpendicular plane the velocities in three directions can be determined using the following equations. x y z P P g 2 T cos cos sin sin cos S m III. RESLTS AN ISCSSIONS.1. Null Technique In this method, yaw angle is set to zero by aligning the probe with the incoming flow (null setting).the Fig. (a-c) shows the calibration curves of the five-hole probe obtained by the null air Fig.. Calibration curves of five-hole probe in null technique.2. Sector Scheme The Fig. shows the pitch and yaw angle map of sectors chosen by the calibration scheme. The symbol indicates the hole registering the maximum pressure. The flow angle α and β are taken within ±. Fig. also indicates the range of α and β for various sensing holes of the probe. It shows that the centre hole (hole 1) covers the most wide range of α and β among all the holes. However, at larger angles of α and β other holes are likely to sense the total pressure and hence pressure sensed by the holes at their location is maximum. Further, the centre hole or other holes at this position will become stalled. The contours show lines of increasing pressure as the holes of the probe is oriented to the flow. The curvature of the lines increases as the pressure increases, since the flow is more directly into the hole and exhibits grater dependence upon the P a g e

5 Ratneswar Majumdar et al. Int. Journal of Engineering Research and Applications ISSN: , Vol. 6, Issue, (Part - 7) May 16, pp.27-2 inclination of the hole with respect to the mean flow Fig.. Sector map of pitch and yaw angle of fivehole probe The Fig.6(a-e) shows the contours of the response of the individual five pressure holes. They are representative of the pressure distribution obtained from the perimeter holes for the probe. The contours as seen are non-symmetric in nature, which may be due to non-symmetry of the holes with respect to the centre hole occurred (c) Pressure hole (a) Pressure hole (b) Pressure hole (d) Pressure hole 2 Fig.6. Pressure holes of Five-hole probe response to pitch and yaw angle IV. CONCLSION 1 P a g e

6 ISSN: , Vol. 6, Issue, (Part - 7) May 16, pp.27-2 The following conclusions are made based on the present study: 1. Null technique is simple during calibration but time consuming at the time of actual measurement. 2. Non-null method, particularly sector scheme is very useful where rotation of the probe is not possible.. Errors in null technique are more as perfect null depends on the least count of the scales associated as well as human skill.. For larger flow angle, sector technique to be a better option. For flow angles within, five-hole probe in non-null technique is very useful. The data reduction technique yielded an accuracy of 1. both in pitch and angle and 1. m/s in velocity. [1]. Bryer,. W. and Pankhurst, Pressureprobe methods for determining wind speed and flow direction, REFERENCES [1]. Pien, P.C., Five hole probe spherical pitot tube, avid Taylor [2]. Model Basin Report 1229, May 198. []. Kjelgaard, S. O., Theoretical erivation and Calibration []. Technique of a Hemispherical-Tipped, Five-Hole Probe, NASA []. Technical Memorandum 7, Sept., [6]. A.L.Treaster and A.M.Yocum, The calibration and application of [7]. five-hole probes, Instrumentation Society of America Trans. [8]. Vol.18, No., pp.2-, [9]. Mukopadha S., utta A., Mallick A.N., and Majumdar B., Effect of five-hole probe tip shape on its calibration, Journal of Aeronautical Society of India, Volume No., No 1. []. Pisasale A. J., Ahmed N.A., A Novel Method for Extending the Calibration Range of Five-Hole Probe for Highly Three-imensional Flows. Flow Measurement and Instrumentation 1, March 2. [11]. Sitaram.N, and Treaster, A.L, A simplified method of using four- hole probe to measure three-dimensional flow field, J. Fluid., Vol. 7, No 1, pp 1-, 198. [12]. Netter.J and Washerman.W, Simple regression model in matrix terms, Applied linear Statistical Models, Richard.Irwin, Inc, III, pp, 197. [1]. Chowdhury,., "Modeling and calibration of pressure probes", M.P.E. Thesis, Jadavpur niversity, 7. 2 P a g e